LEBEDINSKOYE, Ukraine — The cease-fire between the Ukrainian government and Russian-backed separatists appeared in danger Saturday after just a day as several artillery barrages resumed around the city of Mariupol.

Soldiers and civilians who have been enduring life on the front lines said they doubted that the cease-fire, which came into effect on Friday, would hold after five months of warfare.

The sound of artillery strikes were heard late Saturday on the edge of Mariupol, which Ukrainian forces have been in danger of losing, according to reporters in the city. The barrages started around midnight, but later stopped. It was not immediately clear who had been responsible for the shelling, but some reports, which could not be independently confirmed, suggested that Ukrainian government positions had come under attack. The official Twitter account of the pro-Russian rebels said fighting was underway in Mariupol and that rebel positions had come under fire. Nevertheless, a prisoner exchange was going ahead at dawn, another Twitter post said, referring to one of the terms of the cease-fire agreement.

Despite assurances from President Petro O. Poroshenko that the agreement would keep Ukraine whole, there has been concern in Ukraine that Russia, after using its army to deal a military blow against Ukrainian troops, was dictating terms that would keep a significant portion of the country under its sway. It will largely be up to Mr. Poroshenko — who was elected in May on a platform of ending the war in two weeks and who faces parliamentary elections on Oct. 26 — to rapidly convince Ukrainians that negotiating with the separatists was their best choice.

“Ukrainian public opinion is not ready for a peace that does not reflect Ukrainian aspirations,” said Mykhailo Minakov, a professor at the University of Kiev-Mohyla Academy and a civil rights activist. “They are not ready to respect an agreement that would respond to the demands of the separatists or the Russians.”

Each side claimed that the other had committed about 10 cease-fire violations, but most of the breaches seemed to occur immediately after the 6 p.m. deadline for the truce on Friday, or they involved small-arms fire.

Col. Andriy Lysenko, the spokesman for Ukraine’s National Security and Defense Council, told a briefing in Kiev on Saturday that the southeast was “generally calmer” and that the Ukrainian forces had not suffered any losses since the cease-fire went into effect.

Vladimir Kononov, the defense minister of the self-declared pro-Russian Donetsk People’s Republic, said in an interview that nine cease-fire breaches overnight had left 10 of his men wounded. “If they go on breaking it, we will have to fire in response,” he said.

President Vladimir V. Putin of Russia and Mr. Poroshenko spoke by telephone Saturday, according to a statement on Mr. Poroshenko’s website, with both affirming that the cease-fire was holding. They also discussed next steps, though they did not publicly specify them.

In Moscow, the Russian Foreign Ministry issued a statement blasting a threat of further sanctions from the European Union on the very day a cease-fire was declared.

Mr. Poroshenko said on Friday that the agreement mirrored both a recent peace plan proposed by Mr. Putin and his own proposal from June. He said it included steps for an immediate cease-fire and promises of greater self-government for the separatist regions.

The last part is likely to be the most difficult for the public to accept since there was already the impression that Mr. Putin had won by leaving his proxy force in place. Russia has long denied sending troops or weapons into Ukraine.

Many believe that that Mr. Putin seeks to create a frozen conflict — much as Russia did in Georgia and Moldova — to keep Ukraine permanently destabilized with a breakaway region in its southeast corner. Since March, Moscow has demanded that Ukraine put in place a federal system that would give regions significant autonomy, including the ability to establish their own foreign policy.

But Ukraine has promised “decentralization” without really defining publicly what that means.

“We are ready to provide significant steps including the decentralization of power, including the special status for certain districts in the Donetsk and Luhansk region for economic freedom,” Mr. Poroshenko told a news conference at the NATO summit meeting in Wales after the cease-fire agreement was announced. But he concluded by stressing that the peace process was based on preserving “the sovereignty, territorial integrity and independence of my country.”

Those who have discussed the issue with Mr. Poroshenko said regional autonomy was not part of his thinking, even if Russia and Mr. Putin in particular had used the term repeatedly.

Yevhen Bystrytsky, the executive director of the International Renaissance Foundation, part of the Open Society Foundations established by the billionaire investor and philanthropist George Soros, said the seeming lack of consensus was a problem. Still, he noted that initial Russian news reports about the truce had also used the word “decentralization.”

In any case, he said the priority now was to stop the killing, in a conflict that the United Nations says has left more than 2,600 people dead. “The principal issue is not to clarify both interpretations,” he said. “The idea is to stop the war and then agree on something more.”

Both the Ukrainian Foreign Ministry and the prime minister’s office declined to comment. There was not even consensus on the number of points agreed to at the negotiations in Belarus. Mr. Poroshenko said in Wales that there were 12, but his appointee, the governor of Donetsk, Sergei Taruta, put the number at 14.

“The key priority right now is to get our hostages back,” said Vladimir Garkavenko, a spokesman for Mr. Poroshenko. “The future of these regions is that they will remain a peaceful part of Ukrainian territory, but when this will happen is unclear.”

For people in the east, there seemed to be uncertainty even about the coming hours.

In Lebedinskoye on Saturday, one family expressed its lack of confidence by bundling children and belongings into a car and fleeing. Like others, they heard explosions in the distance and believed rumors that barrages that had killed a woman and two children here on Friday would soon resume.

On the main road, Ukrainian soldiers still manned checkpoints, checking cars and documents. A reconnaissance unit stopped on a hill to scout for enemy movement. “It’s too early to relax,” one soldier said.

The woman fleeing by car with her family said the deaths a day earlier had rattled her. “We are going,” said the woman, who gave only her first name, Marina. “There was a strike behind that house and there are dead bodies there, and they say at noon there will be shelling.”

The village stands on the front line between rebel fighters and Ukrainian military defenses. It was the scene of a last spurt of fighting on Friday, when eight rockets slammed down just hours before the cease-fire was declared. Bloodstains marked where the two children who were killed had fallen as they ran toward an underground shelter.

On Saturday morning the area was quiet. Civilians were outside clearing up bomb damage and driving and monitors from the Organization for Security and Cooperation in Europe were out too.

For the people in this village and the one next door, Shirokino, the lull was almost as nerve-racking as the fighting. “The most fearful thing is the silence between bombings,” said Natalia Logozinskaya, a shopkeeper, standing in the wreckage of a neighbor’s house that had been hit by a shell.

Most people had spent the past two days cowering in their basements. The villages stand on the road from Novazovsk — a town seized by Russian-backed rebels late last month — and Mariupol.

Mrs. Logozinskaya said that whether they supported Russia or Ukraine, most villagers just wanted the fighting to stop. “I really hope the peace can hold,” she said. “I cannot believe that there is such a big issue that they cannot compromise.”

Correction:

An earlier version of a picture caption with this article misstated the reason members of a family fled their home in the southeastern Ukrainian village of Lebedinskoye. They did so because they heard explosions, not shelling. The article also misspelled the surname of a spokesman for President Petro O. Poroshenko of Ukraine. He is Vladimir Garkavenko, not Garkavanko.

A version of this article appears in print on , on Page A9 of the New York edition with the headline: Cease-Fire in Ukraine Is Shaken as Violations Are Reported in Southeast. Order Reprints | Today’s Paper | Subscribe